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Research Activities > Programs > Fast Approximate Algorithms > Gregory Beylkin

Fast Multipole Method, Tree-Code and Related Approximate Algorithms.
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Separated Representations and Fast Adaptive Algorithms in Multiple Dimensions

Dr. Gregory Beylkin

University of Colorado at Boulder

Abstract:   In the ordinary representation the cost of linear algebra operations, such as matrix-matrix or matrix-vector multiplications, increases exponentially with the underlying physical dimension. For any finite but arbitrary accuracy, we represent operators in a separated form, a numerical generalization of separation of variables. Our approach is based on the fact that a wide class of physically significant operators have a low separation rank. I will present relevant analytic and numerical results and describe a new method for electron structure computations based on this approach.